Second-Order Propositional Satisfiability

Program synthesis is the automated construction of software from a specification. While program synthesis is undecidable in general, we show that synthesising finite-state programs is NEXPTIMEcomplete. We then present a fully automatic, sound and complete algorithm for synthesising C programs from a specification written in C. Our approach uses a combination of bounded model checking, explicit-state model checking and genetic programming to achieve surprisingly good performance for a problem with such high complexity. By identifying a correspondence between program synthesis and secondorder logic, we show how to use our program synthesiser as a decision procedure for existential second-order logic over finite domains. We illustrate the expressiveness of this logic by encoding several program analysis problems including superoptimisation, de-obfuscation, safety and termination. Finally, we present experimental results showing that our approach is tractable in practice.